Order = 322560 = 2^{10}.3^{2}.5.7.

Mult = 2.

Out = 1.

## Porting notes

Fully copied from version 2. 30/7/06.## Standard generators

Standard generators of 2^{4}.A_{8} are *a*, *b* where *a* is in class 3A, *b* has order 7, *a**b* has order 6, [*a*, *b*] has order 2 and *a**b**a**b*^{2}*a**b*^{5} has order 6. Alternatively: *a* is in class 3A, *b* has order 7, *a**b* has order 6, *a**b*^{3} has order 12 and *a**b**a**b*^{2}*a**b*^{5} has order 6.

Standard generators of 2^{4}.2A_{8} are preimages *A*, *B* where *A* has order 3 and *B* has order 7.

## Presentations

Group | Presentation | Link |
---|---|---|

2^{4}.A_{8}
| 〈 a, b | a^{3} = b^{7} = (ab)^{6} = [a, b]^{2} = abab^{2}a^{−1}bab^{−2}ab^{3}ab^{−3}ab^{−3} = 1 〉
| Details |

## Representations

### Representations of 2^{4}.A_{8}

- View detailed report.
- Permutation representations:
Number of points ID Generators Description Link 30 Std Details 128 Std Details - Matrix representations
Char Ring Dimension ID Generators Description Link 0 Z 15 Std Details 2 GF(2) 11 a Std uniserial module 4.6.1 Details 2 GF(2) 11 b Std uniserial module 1.6.4 Details 3 GF(3) 15 Std Details 5 GF(5) 15 Std Details 7 GF(7) 15 Std Details